Mean-variance Optimization Research Articles

Portfolio selection revisited

AbstractIn 1952, Harry Markowitz formulated portfolio selection as a trade-off between expected, or mean, return and variance. This launched a massive research effort devoted to finding suitable inputs to mean-variance optimization. The estimation problem is high dimensional and a factor model is at the core of many attempts. A factor model can reduce the number of parameters that need to be estimated to a manageable size, but these parameters may incorporate substantial, hidden estimation error. Recent analysis elucidates the nature of this error, identifies a mechanism by which it can corrupt optimization and provides a method for its mitigation. We explore this analysis here by illustrating how to improve the volatility ratio of large optimized portfolios, leading to superior portfolio selection.$$^{*}$$ ∗

Optimization of Renewable Energy Company Stock Portfolio for Investment Decision Making using the Markowitz Model

This study focuses on optimizing the renewable energy company's stock portfolio using the Markowitz model, which aims to balance risk and return for proper investment decision making. With the increasing demand for clean energy, portfolio optimization in the renewable energy sector is important for investors. This research takes into account historical stock performance and applies the Mean-Variance Optimization framework to minimize risk while maximizing return. This portfolio consists of selected renewable energy companies, and the analysis runs from September 2021 to August 2024. This study aims to analyze the allocation of investment portfolios in renewable energy company stocks in Indonesia. Based on the analysis results, the investment portfolio is allocated to five main stocks, namely BUMI.JK with an investment value of IDR 17,075,844 (17.08%), INDY.JK of IDR 5,825,852 (5.83%), KEEN.JK of IDR 33,766,798 (33.77%), RAJA.JK of IDR 43,084,876 (43.08%), and WIKA.JK of IDR 246,630 (0.25%). These results indicate that most of the funds are invested in RAJA.JK and KEEN.JK stocks, which contribute more than 75% of the total investment portfolio

Mesoscopic structure of the stock market and portfolio optimization

AbstractThe idiosyncratic and systemic components of market structure have been shown to be responsible for the departure of the optimal mean-variance allocation from the heuristic ‘equally weighted’ portfolio. In this paper, we exploit clustering techniques derived from Random Matrix Theory to study a third, intermediate (mesoscopic) market structure that turns out to be the most stable over time and provides important practical insights from a portfolio management perspective. First, we illustrate the benefits, in terms of predicted and realized risk profiles, of constructing portfolios by filtering out both random and systemic co-movements from the correlation matrix. Second, we redefine the portfolio optimization problem in terms of stock clusters that emerge after filtering. Finally, we propose a new wealth allocation scheme that attaches equal importance to stocks belonging to the same community and show that it further increases the reliability of the constructed portfolios. Results are robust across different time spans, cross sectional dimensions and set of constraints defining the optimization problem.

Integrating LSTM Networks with Mean-Variance Optimization for Enhanced Portfolio Construction: An Empirical Study on UK Stock Market

Portfolio optimization has long been a central theme in finance. With ongoing advancements in machine learning, there is a significant opportunity to integrate predictive methods into portfolio optimization. This paper proposes leveraging Long Short-Term Memory (LSTM) networks alongside the established Mean-Variance (MV) optimization framework to construct optimal portfolios. These portfolios aim to help financial investors effectively manage and mitigate risk while maximizing returns. The study meticulously screened the leading stocks of 12 prominent UK companies listed on the London Stock Exchange (LSE), known for their influence and visibility. Initially, the study applies the LSTM networks to predict stock price volatility and integrates these predictions into the MV model to allocate portfolio weights effectively. To underscore the superiority of the proposed approach, the study compares cumulative returns from portfolios optimized for maximum and minimum variance Sharpe ratios with real data against the FTSE100 index over the same period. The results demonstrate that the portfolio optimized with the maximum Sharpe ratio significantly outperforms both the conservative minimum variance portfolio and the FTSE100 index. This empirical evidence underscores the practical value of integrating advanced machine learning techniques with established financial theory, enabling more innovative and efficient investment strategies to meet the evolving needs of financial investors.

Portfolio Optimization Using LSTM for Five Selected Stocks

Portfolio construction is very critical in the financial markets as it assists investors in achieving maximum returns with minimum risks through diversification. In this paper, Long Short-Term Memory (LSTM) models are employed to predict stock prices and optimize investment portfolios. Historical adjusted closing prices from Yahoo Finance for the period from January 1, 2023, to March 1, 2024, were used to predict the future stock prices of Apple Inc. (AAPL), Microsoft Corporation (MSFT), BlackRock Inc. (BLK), JPMorgan Chase & Co. (JPM), and Tesla Inc. (TSLA) using LSTM models. Portfolios were constructed using mean-variance optimization based on these predictions, and Monte Carlo simulations were employed to capture the uncertainty around the estimates. The results are treasured for investors in financial markets as they spotlight the limitations and capability risks of depending totally on gadget learning predictions for portfolio optimization. This emphasizes the want for a greater comprehensive method to investment decision-making that considers more than one factors and methodologies.

Integration of prediction and optimization for smart stock portfolio selection

Machine learning (ML) algorithms pose significant challenges in predicting unknown parameters for optimization models in decision-making scenarios. Conventionally, prediction models are optimized independently in decision-making processes, whereas ML algorithms primarily focus on minimizing prediction errors, neglecting the role of decision-making in downstream optimization tasks. The pursuit of high prediction accuracy may not always align with the goal of reducing decision errors. The idea of reducing decision errors has been proposed to address this limitation. This paper introduces an optimization process that integrates predictive regression models within a mean–variance optimization setting. This innovative technique introduces a general loss function to capture decision errors. Consequently, the predictive model not only focuses on forecasting unknown optimization parameters but also emphasizes the predicted values that minimize decision errors. This approach prioritizes decision accuracy over the potential accuracy of unknown parameter prediction. In contrast to traditional ML approaches that minimize standard loss functions such as mean squared error, our proposed model seeks to minimize the objective value derived directly from the decision-making problem. Furthermore, this strategy is validated by developing an optimization-based regression tree model for predicting stock returns and reducing decision errors. Empirical evaluations of our framework reveal its superiority over conventional regression tree methods, demonstrating enhanced decision quality. The computational experiments are conducted on a stock market dataset to compare the effectiveness of the proposed framework with the conventional regression tree-based approach. Remarkably, the results confirm the strengths inherent in this holistic approach.

Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review

Traditional mean-variance (MV) models, considered effective in stable conditions, often prove inadequate in uncertain market scenarios. Therefore, there is a need for more robust and better portfolio optimization methods to handle the fluctuations and uncertainties in asset returns and covariances. This study aims to perform a Systematic Literature Review (SLR) on robust portfolio mean-variance (RPMV) in stock investment utilizing genetic algorithms (GAs). The SLR covered studies from 1995 to 2024, allowing a thorough analysis of the evolution and effectiveness of robust portfolio optimization methods over time. The method used to conduct the SLR followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. The result of the SLR presented a novel strategy to combine robust optimization methods and a GA in order to enhance RPMV. The uncertainty parameters, cardinality constraints, optimization constraints, risk-aversion parameters, robust covariance estimators, relative and absolute robustness, and parameters adopted were unable to develop portfolios capable of maintaining performance despite market uncertainties. This led to the inclusion of GAs to solve the complex optimization problems associated with RPMV efficiently, as well as fine-tuning parameters to improve solution accuracy. In three papers, the empirical validation of the results was conducted using historical data from different global capital markets such as Hang Seng (Hong Kong), Data Analysis Expressions (DAX) 100 (Germany), the Financial Times Stock Exchange (FTSE) 100 (U.K.), S&P 100 (USA), Nikkei 225 (Japan), and the Indonesia Stock Exchange (IDX), and the results showed that the RPMV model optimized with a GA was more stable and provided higher returns compared with traditional MV models. Furthermore, the proposed method effectively mitigated market uncertainties, making it a valuable tool for investors aiming to optimize portfolios under uncertain conditions. The implications of this study relate to handling uncertainty in asset returns, dynamic portfolio parameters, and the effectiveness of GAs in solving portfolio optimization problems under uncertainty, providing near-optimal solutions with relatively lower computational time.

Robust portfolio optimization model for electronic coupon allocation

Currently, many e-commerce websites issue online/electronic coupons as an effective tool for promoting sales of various products and services. We focus on the problem of optimally allocating coupons to customers subject to a budget constraint on an e-commerce website. We apply a robust portfolio optimization model based on customer segmentation to the coupon allocation problem. We also validate the efficacy of our method through numerical experiments using actual data from randomly distributed coupons. Main contributions of our research are twofold. First, we handle six type of coupons, thereby making it extremely difficult to accurately estimate the difference in the effects of various coupons. Second, we demonstrate from detailed numerical results that the robust optimization model achieved larger uplifts of sales than did the commonly-used multiple-choice knapsack model and the conventional mean–variance optimization model. Our results open up great potential for robust portfolio optimization as an effective tool for practical coupon allocation.

ESG integration strategy with a multivariate normal distribution

Purpose: The paper aims to present a new framework for ESG integration strategies in portfolio optimization problems. The optimization in the new structure focuses on the portfolio level, and the procedure is not focused on utility functions or on preliminary weights applied to the asset level. It applies the resampling technique, and all the portfolios are optimal portfolios in the mean-variance space. It uses a filtering process where only optimal portfolios with lower ESG risks are considered. Therefore, this technique works only with optimized portfolios, avoids concentration bias, and considers estimation errors in the expected returns and in the covariance matrix. Design/methodology/approach: The sample mean returns and covariance matrices generated by a multivariate normal distribution are applied in mean-variance optimization to generate several portfolios in the efficient frontiers. An ESG filtering process is used to select portfolios with lower ESG risks from a sample of 42 companies listed on the Brazilian stock exchange with returns from the period of 2018/01/01 to 2024/04/22.Findings: Integration strategy costs may be lower than the best-in-class strategy costs and may be similar to the costs of a negative screening strategy. Social implications: The paper presents a framework that considers social, environmental, and governance factors in the portfolio optimization process.Originality: The main contribution of this paper is to present a new framework that combines resampling of returns’ mean and covariance based on a multivariate normal distribution with an ESG portfolio filtering process.

Portfolio Selection Based on Mean-Generalized Variance Analysis: Evidence from the G20 Stock Markets

Modern finance theories have been increasingly paying attention to nonlinear and asymmetric features of stock returns. In this paper, we extend the concept of covariance to generalized covariance by using Generalized Measure of Correlation (GMC). Based on the generalized covariance which is capable of catching the nonlinearity and asymmetry in stock (index) returns, we propose a mean-generalized variance portfolio selection model which considers the gross-exposure constraint. Furthermore, we propose the corresponding nonparametric estimation approach and the global optimization algorithm to enhance the applicability of our new model. Empirical studies on G20 stock markets support that a portfolio considering nonlinear and asymmetric features among the international markets would outperform traditional ones based on mean-variance optimization and equal weighting strategy in terms of return and flexibility.

Untangling Universality and Dispelling Myths in Mean–Variance Optimization

Untangling Universality and Dispelling Myths in Mean–Variance Optimization

Further Applications of Mean–Variance Optimization

Further Applications of Mean–Variance Optimization

Mean Variance Complex-Based Portfolio Optimization

Mean-Variance (MV) is a method that collects several assets using appropriate weight intending to maximize profits and to reduce risk. Stock market conditions are very volatile, mean variance method does not reach stock market fluctuation well because MV method is only limited to one time period. This study proposes a mean variance complex-based approach that transforms real returns into complex returns by using Hilbert transform to construct an optimal mean-variance portfolio based on complex returns and then find its dynamic asset allocation. The results show that with the same risk tolerance, the mean variance complex-based approach outperforms MV method in profits, losses, and portfolio performance tests.

Portfolio Optimization with Prediction-Based Return Using Long Short-Term Memory Neural Networks: Testing on Upward and Downward European Markets

AbstractIn recent years, artificial intelligence has helped to improve processes and performance in many different areas: in the field of portfolio optimization, the inputs play a crucial role, and the use of machine learning algorithms can improve the estimation of the inputs to create robust portfolios able to generate returns consistently. This paper combines classical mean–variance optimization and machine learning techniques, concretely long short-term memory neural networks to provide more accurate predicted returns and generate profitable portfolios for 10 holding periods that present different financial contexts. The proposed algorithm is trained and tested with historical EURO STOXX 50® Index data from January 2015 to December 2020, and from January 2021 to June 2022, respectively. Empirical results show that our LSTM neural networks are able to achieve minor predictive errors since the average of the MSE of the 10 holding periods is 0.00047, the average of the MAE is 0.01634, and predict the direction of returns with an average accuracy over the 10 investment periods of 95.8%. Our prediction-based portfolios consistently beat the EURO STOXX 50® Index, achieving superior positive results even during bear markets.

Practical Improvements to Mean-Variance Optimization for Multi-Asset Class Portfolios

In the more than 70 years since Markowitz introduced mean-variance optimization for portfolio construction, academics and practitioners have documented numerous weaknesses in the approach. In this paper, we propose two easily understandable improvements to mean-variance optimization in the context of multi-asset class portfolios, each of which provides less extreme and more stable portfolio weights. The first method sacrifices a small amount of expected optimality for reduced weight concentration, while the second method randomly resamples the available assets. Additionally, we develop a process for testing the performance of portfolio construction approaches on simulated data assuming variable degrees of forecasting skill. Finally, we show that the improved methods achieve better out-of-sample risk-adjusted returns than standard mean-variance optimization for realistic investor skill levels.

Robust time-consistent strategies of DC pension plans with the return of premiums clauses under inflation

. This article investigates the robust time-consistent investment strategy for a DC pension plan with model uncertainty under the mean-variance optimization objective. For the avoidance of reductions in investment returns due to inflation risk and premature death of members, an inflation-indexed bond is introduced into the financial market and a return of premium clause is incorporated into the model. By establishing extended Hamilton-Jacobi-Bellman (HJB) equations, the explicit solutions of both the robust precommitment strategy and the robust time-consistent strategy are presented by virtue of the robust optimal control theory and the stochastic dynamic programming approach. Furthermore, two degradation cases are derived in detail. Finally, a numerical example demonstrates the analysis of the obtained results.

Optimizing Portfolio Construction Using Nifty India Manufacturing Index: A Risk-Return Analysis with Python

This paper presents a comprehensive analysis of portfolio construction strategies aimed at maximizing risk-adjusted returns for investors. Utilizing historical data on stock returns and risks, a meticulous selection process was employed to identify 15 stocks with superior risk-return profiles. These stocks were chosen based on their outperformance relative to the dataset's average measures, prioritizing returns higher than the dataset average and risks lower than average risk levels. The selected stocks, representing a diverse range of manufacturing-related businesses, formed the cornerstone of an optimal portfolio designed to minimize sector-specific risks while maximizing growth potential. Through rigorous portfolio optimization techniques, including Markowitz's mean-variance optimization, the study identified an optimal portfolio allocation with a return of 50.22% and volatility of 13.33%. Insights from the study offer valuable perspectives for investors seeking realistic and sustainable wealth accumulation strategies. The research also identifies avenues for future exploration, including the integration of alternative asset classes, behavioral finance insights, and advancements in risk management technologies. This study demonstrates the effectiveness of Python in financial analysis and portfolio optimization while furthering the theory of portfolios and providing valuable guidance for making investment decisions. Keywords: Returns, Risk, Volatility, Optimal Portfolio Construction, Manufacturing Sector, Markowitz Portfolio Theory,

Optimizing Portfolio Allocation in the Indian Defense Sector: A Python-Based Approach

This paper presents a detailed analysis of portfolio construction strategies aimed at maximizing risk-adjusted returns for investors, utilizing Python-based methodologies. By leveraging historical data on stock returns and risks, a meticulous selection process identified 5 stocks with superior risk-return profiles, outperforming the dataset's average measures with higher returns and lower risks. The selected stocks from the defense industry formed the foundation of an optimal portfolio designed to minimize sector-specific risks while maximizing growth potential. Through rigorous portfolio optimization techniques, including Markowitz's mean-variance optimization, an optimal portfolio allocation was identified with a return of 62.40% and volatility of 27.74%. Insights from the study provide valuable perspectives for investors seeking realistic and sustainable wealth accumulation strategies. The research also highlights future avenues for exploration, such as integrating alternative asset classes, incorporating behavioral finance insights, and leveraging advancements in risk management technologies. This study contributes to advancing portfolio theory and offers practical guidance for investment decision-making.This study demonstrates the effectiveness of Python in financial analysis and portfolio optimization while furthering the theory of portfolios and providing valuable guidance for making investment decisions. Keywords: Returns, Risk, Volatility, Optimal Portfolio Construction, Defense Sector, Markowitz Portfolio Theory,

The Number of Stocks Before (n) and After Portfolio Optimization (k): The Heuristic k ≈ sqrt(n)

This study focuses on the relationship between the number of securities (n) pre-selected for mean-variance portfolio optimization and the number of optimal securities (k). We propose a heuristic k ≈ square root (n) based on empirical research optimizing different sized (n) portfolios. That is, a sample selection of 20-30 securities should yield a portfolio of about five optimal securities, and an initial sample of 500 securities, should result in an optimal portfolio of about 22. We focus on the tangent portfolio that maximizes the return-to-risk ratio. The heuristic finds its support, rationale, and logic in the numerical properties and statistical nature of the optimization. More specifically, the heuristic seems to originate in the dynamic convergence patterns observable in many statistical processes, especially in standard deviations. It is also supported by available results in the literature. Our “square root” heuristic functions as part of the wider family of approximation around the power law, where some variables (authors, securities, people) receive a disproportionate share of a given collection of items – see, for example, Pareto’s principle, Zipf’s law, Lotka’s law, Price’s square root law, Simon’s law, etc. The heuristic provides assistance not only in anticipating the number of optimal securities chosen by the mean-variance optimizer but also in suggesting selectivity in the effort of pre-selecting securities prior to the optimization and in sharpening portfolio-based approaches to investing in general. In sum, the heuristic k ≈ sqrt(n) seems helpful at all levels of portfolio management.

Optimizing Cryptocurrency Portfolios: A Comparative Study of Rebalancing Strategies

Objective – This study aims to contribute to the field of cryptocurrency portfolio management and rebalancing strategies by empirically investigating the impact of different allocation frequencies and threshold percentages on the risk-adjusted returns of cryptocurrency portfolios. Methodology/Technique – Utilizing a simulation of 10,000 cryptocurrency portfolios comprising seven assets, including Ethereum (ETH), Bitcoin (BTC), Tether (USDT), Litecoin (LTC), Solana (SOL), Dogecoin (DOGE), and Polygon (MATIC), this study examines and compares the effects of different allocation frequencies (daily, weekly, and monthly) in time-based rebalancing and various threshold percentages (5%, 10%, and 15%) in threshold-based strategies on the portfolios' risk-adjusted returns, using the Sharpe ratio. The performance of these strategies is also compared with a passive buy-and-hold strategy. Findings –The research reveals statistically significant differences in the risk-adjusted returns between the buy-and-hold strategy and the daily rebalancing and threshold-based strategies with 5% and 10% threshold percentages. The daily rebalancing strategy demonstrates a higher Sharpe ratio, while lower threshold percentages lead to better risk-adjusted returns. Novelty – These empirical findings, using a simulation of 10,000 cryptocurrency portfolios, provide valuable insights into optimizing cryptocurrency portfolio performance through rebalancing strategies. Additionally, they highlight the effectiveness of implementing rebalancing techniques in cryptocurrency portfolios, contributing to the understanding of rebalancing optimization in this domain. Type of Paper: Empirical JEL Classification: G11, G19. Keywords: Cryptocurrency; Mean-Variance Optimization; Portfolio Management; Rebalancing Strategies; Risk-Adjusted Returns Reference to this paper should be made as follows: Sornmayura, S; Sakolvieng, N; Numgaroonaroonroj, K. (2024). Optimizing Cryptocurrency Portfolios: A Comparative Study of Rebalancing Strategies, J. Fin. Bank. Review, 8(4), 01 – 16. https://doi.org/10.35609/jfbr.2024.8.4(1)